Journal of Mathematics Researchhttp://www.ccsenet.org/journal/index.php/jmr
<p><strong><em>Journal of Mathematics Research </em></strong>(ISSN: 1916-9795; E-ISSN 1916-9809) is an open-access, international, double-blind peer-reviewed journal published by the Canadian Center of Science and Education. This journal, published <strong>bimonthly</strong> (<span>February, April, June, August, October and December</span>) in <strong>both print and online versions</strong>, keeps readers up-to-date with the latest developments in all aspects of mathematics.</p><div class="Section1"><strong>The scopes of the journal </strong>include, but are not limited to, the following topics: statistics, approximation theory, numerical analysis, operations research, dynamical systems, mathematical physics, theory of computation, information theory, cryptography, graph theory, algebra, analysis, probability theory, geometry and topology, number theory, logic and foundations of mathematics. <em> </em></div><div class="Section1"><p>This journal accepts article submissions<strong> <a href="/journal/index.php/jmr/information/authors">online</a> or by <a href="mailto:jmr@ccsenet.org">e-mail</a> </strong>(jmr@ccsenet.org).</p></div><div class="Section1"><br /><br /><strong><strong><em><img src="/journal/public/site/images/jmr/jmr.jpg" alt="jmr" width="201" height="264" align="right" hspace="20" /></em></strong><strong>ABSTRACTING AND INDEXING:</strong></strong></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><ul><li>BASE (Bielefeld Academic Search Engine)<strong><br /></strong></li><li><strong>EBSCOhost</strong></li><li>Google Scholar</li><li>JournalTOCs</li><li>LOCKSS</li><li><strong>MathEDUC</strong></li><li><strong><a href="http://www.ams.org/dmr/JournalList.html">Mathematical Reviews</a>® (<a href="http://www.ams.org/mathscinet">MathSciNet</a>®) </strong>(-2012)</li><li>MathGuide</li><li>NewJour</li><li>OCLC Worldcat</li><li>Open J-Gate</li><li>SHERPA/RoMEO</li><li>Standard Periodical Directory</li><li>Ulrich's</li><li>Universe Digital Library</li><li><strong><a href="https://zbmath.org/journals/?q=se:00006772">Zentralblatt MATH</a> </strong>(2009-2013)</li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"> </div>Canadian Center of Science and Educationen-USJournal of Mathematics Research1916-9795Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication. <br />Copyrights for articles published in CCSE journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.

Augmented Stabilized and Galerkin Least Squares Formulationshttp://www.ccsenet.org/journal/index.php/jmr/article/view/62499
We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving problems as opposed to div-stable pairs used earlier. Higher order spectral/$hp$ approximations are utilized for solving two dimensional computational fluid dynamics (CFD) problems with the new formulations named as the Augmented SUPS (ASUPS) and Augmented Galerkin Least Squares (AGLS) formulations. Excellent conservation of mass properties are observed for the<br />problem with open boundaries in confined enclosures. Inexact Newton Krylov methods are used as the non-linear solvers of choice for the problems studied. Faithful representations<br />of all fields of interest are obtained for the problems tested.Rakesh RanjanYusheng FengAnthony Theodore Chronopolous
Copyright (c) 2016 Anthony Theodore Chronopoulos
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2016-11-252016-11-2586110.5539/jmr.v8n6p1Approximation of a Second-order Elliptic Equation with Discontinuous and Highly Oscillating Coefficients by Finite Volume Methodshttp://www.ccsenet.org/journal/index.php/jmr/article/view/62607
In this paper we consider the numerical approximation of a class of second order elliptic boundary value problems with discontinuous and highly periodically oscillating coefficients. We apply both classical and modified finite volume methods for the approximate solution of this problem. Error estimates depending on $\varepsilon$ the parameter involved in the periodic homogenization are established. Numerical simulations for one-dimensional problem confirm the theorical results and also show that the modified scheme has a smaller constant of convergence than the classical scheme based on harmonic averaging for this class of equations.Bienvenu Ondami
Copyright (c) 2016 Bienvenu ONDAMI
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2016-11-252016-11-25863410.5539/jmr.v8n6p34Computable Error Bounds for a Class of Boundary Value Problems: a Coefficients Perturbation Approachhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62671
This paper is concerned with computing upper and lower bounds for the error committed when some boundary value problems are approximated by means of numerical techniques based on the Coefficients Perturbation Methods. These computed bounds are expressed in terms of the perturbations introduced in the differential equation and in the prescribed boundary conditions associated with it. Numerical examples demonstrating the sharpness of our results are given.Mohamed K. El DaouAhmad R. Al-Hamdan
Copyright (c) 2016 Mohamed K. El Daou, Ahmad R Al-Hamdan
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2016-11-252016-11-25864510.5539/jmr.v8n6p45Pollution Transfer as Optimal Mass Transport Problemhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62766
In this paper, we use mass transportation theory to study pollution transfer in porous media. We show the existence of a $L^2-$regular vector field defined by a $W^{1, 1}-$ optimal transport map. A sufficient condition for solvability of our model, is given by a (non homogeneous) transport equation with a source defined by a measure. The mathematical framework used, allows us to show in some specifical cases, existence of solution for a nonlinear PDE deriving from the modelling. And we end by numerical simulations.L. NdiayeMb. NdiayeA. SyD. Seck
Copyright (c) 2016 SY Alassane
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2016-11-252016-11-25865810.5539/jmr.v8n6p58Geometry of the 3D Pythagoras' Theoremhttp://www.ccsenet.org/journal/index.php/jmr/article/view/64646
This paper explains step-by-step how to construct the 3D Pythagoras' theorem by geometric manipulation of the two dimensional version. In it is shown how $x+y=z$ (1D Pythagoras' theorem) transforms into $x^2+y^2=z^2$ (2D Pythagoras' theorem) via two steps: a 90-degree rotation, and a perpendicular extrusion. Similarly, the 2D Pythagoras' theorem transforms into 3D using the same steps. Octahedrons emerge naturally during this transformation process. Hence, each of the two dimensional elements has a direct three dimensional equivalent. Just like squares govern the 2D, octahedrons are the basic elements that govern the geometry of the 3D Pythagoras' theorem. As a conclusion, the geometry of the 3D Pythagoras' theorem is a natural evolution of the 1D and 2D. This interdimensional evolution begs the question -- Is there a bigger theorem at play that encompasses all three?Luis Teia
Copyright (c) 2016 Luis Teia
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2016-11-252016-11-25867810.5539/jmr.v8n6p78Mathematical Models of Refugee Immigration and Recommendations of Policieshttp://www.ccsenet.org/journal/index.php/jmr/article/view/64647
<p><span lang="EN-US">Over the past two years, <span>the refugee crisis resulted from the racial conflict, persecution, generalized violence and violations of human rights has forced an enormous </span>number of refugees to flee to Europe. Aiming to address the problem caused by the flow of refugees, we analyzed the actual procedure of their movement and divide it into three major stages. We designed the gathering model, the entering model, the transferring model, even the health and safety model. Finally, we used the models described above to complete our assigned tasks. Also we put forward seven major policy recommendations to the committee. We accompanied every policy with a straightforward explanation so that people without any technical background can easily understand our insights. The main strength of our model is that it can forecast the flow of immigration and provide meaningful suggestions policies for refugees. With the help of modern computing software, we can track the current tendency and make judges efficiently.</span></p>Qilong ChengTiancheng YuJingkai YanRu Wang
Copyright (c) 2016 Qilong Cheng, Tiancheng Yu, Jingkai Yan, Ru Wang
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2016-11-252016-11-25868510.5539/jmr.v8n6p85Discovery of Similarity and Dissimilarityhttp://www.ccsenet.org/journal/index.php/jmr/article/view/64648
<p><span lang="EN-US">The<span> aim</span> <span>o</span>f this pap<span>e</span>r is to <span>i</span>ntrodu<span>c</span>esome<span> a</span>ppl<span>ic</span><span>a</span>t<span>i</span>ons on si<span>m</span>i<span>l</span><span>a</span>rities <span>a</span>nd dis<span>s</span>i<span>m</span>i<span>l</span><span>a</span>rities. Usingof asi<span>m</span>pl<span>i</span>fi<span>e</span>d d<span>i</span><span>a</span><span>g</span><span>r</span><span>a</span>m andtabl<span>e</span>s to present the information about thes<span>i</span>m<span>i</span>la<span>r</span>i<span>t</span>ies <span>a</span>nd dis<span>s</span>i<span>m</span>i<span>l</span><span>a</span>rities <span>acc</span>ount pro<span>ce</span>ss and o<span>r</span>g<span>a</span>ni<span>z</span><span>a</span>t<span>i</span>on <span>a</span><span>r</span>e<span> a</span>lso e<span>a</span><span>s</span>y<span>a</span>nd we<span>ca</span>lcu<span>l</span><span>a</span>ted thetopo<span>l</span>o<span>g</span>y b<span>a</span>s<span>e</span>d on the simi<span>l</span><span>a</span>ri<span>t</span>y<span>a</span>nd topo<span>l</span>o<span>g</span>yvie<span>w</span>s of thed<span>i</span>ss<span>i</span>m<span>i</span>la<span>r</span>i<span>t</span><span>y</span>.<span>F</span>orinfo<span>r</span><span>m</span><span>a</span>t<span>i</span>on <span>s</span><span>y</span>stem whose v<span>a</span>lues <span>a</span><span>r</span>enume<span>r</span>ic,am<span>e</span>thod of <span>c</span>lassifi<span>ca</span>t<span>i</span>on is sug<span>g</span><span>e</span>sted.This <span>m</span><span>e</span>thod <span>i</span>s bas<span>e</span>d on <span>c</span>onstru<span>c</span>t<span>i</span>ng<span>n</span><span>e</span><span>i</span><span>g</span>hbor<span>h</span><span>o</span>od r<span>e</span>lation on <span>t</span>heunive<span>r</span><span>s</span>eof the<span>r</span><span>e</span>sul<span>t</span><span>e</span>d <span>c</span>lassifi<span>c</span><span>a</span>t<span>i</span>on not <span>g</span><span>e</span><span>n</span><span>e</span>r<span>a</span>l<span>l</span>ya p<span>a</span>rtit<span>i</span>on f<span>o</span>r theunive<span>r</span>s<span>e</span>.</span></p>T. N. AlharthiM. A. Elsafty
Copyright (c) 2016 T. N. Alharthi, M. A. Elsafty
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2016-11-252016-11-258610510.5539/jmr.v8n6p105Efficiency Analysis of Public Transportation Subunits Using DEA and Bootstrap Approaches -- Dakar Dem Dikk Case Studyhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62931
Transportation is a sector which plays an important role in the process of development of countries around the world. A crucial step in transportation planning process is the measure of the efficiency of transportation systems in order to guarantee the desired service. This paper investigates the relative efficiencies of lines of the main public transportation company Dakar Dem Dikk (DDD)\footnote{\textit{Dem Dikk} meaning \guillemotleft Go-Return\guillemotright} in Dakar (Senegal). The objective is to apply Data Envelopment Analysis (DEA) and bootstrapping approaches in order to identify opportunities for improvement. In this study, we examine technical efficiency for the 24 lines of DDD using Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) DEA output oriented models. We apply bootstrap approach for bias correction and for confidence intervals creation of our estimates. Finally, we examine the returns to scale characterization of lines. The results establish that there exist possibilities for improvement for the lines and also shown that there are potential for restructure for some lines.Oumar SowAmar OukilBabacar M. NdiayeAboubacar Marcos
Copyright (c) 2016 Babacar Mbaye Ndiaye, Oumar Sow, Aboubacar Marcos, Amar Oukil
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2016-11-252016-11-2586114The Fundamental Matrix of the Simple Random Walk with Mixed Barriershttp://www.ccsenet.org/journal/index.php/jmr/article/view/63286
The simple random walk with mixed barriers at state $ 0 $ and state $ n $ defined on non-negative integers has transition matrix $ P $ with transition probabilities $ p_{ij} $. Matrix $ Q $ is obtained from matrix $ P $ when rows and columns at state $ 0 $ and state $ n $ are deleted . The fundamental matrix $ B $ is the inverse of the matrix $ A = I -Q $, where $ I $ is an identity matrix. The expected reflecting and absorbing time and reflecting and absorbing probabilities can be easily deduced once $ B $ is known. The fundamental matrix can thus be used to calculate the expected times and probabilities of NCD's.Yao Elikem AyekpleDerrick Asamoah OwusuNana Kena FrempongPrince Kwaku Fefemwole
Copyright (c) 2016 YAO ELIKEM AYEKPLE, DERRICK OWUSU ASAMOAH, NANA KENA FREMPONG, PRINCE KWAKU FEFEMWOLE
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2016-11-252016-11-258612810.5539/jmr.v8n6p128Some Bounds for the Norms of Circulant Matrices with the k-Jacobsthal and k-Jacobsthal Lucas Numbershttp://www.ccsenet.org/journal/index.php/jmr/article/view/64650
In this paper we investigate upper and lower bounds of the norms of the<br />circulant matrices whose elements are $k-$Jacobsthal numbers and $k-$%<br />Jacobsthal Lucas numbers.Sukran Uygun
Copyright (c) 2016 Sukran Uygun
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2016-11-252016-11-258613310.5539/jmr.v8n6p133The Risk Averse Investor's Equilibrium Equity Premium in a Semi Martingale Market with Arbitrary Jumpshttp://www.ccsenet.org/journal/index.php/jmr/article/view/62405
In this paper, we study the risk averse investor's equilibrium equity premium in a semi martingale market with arbitrary jumps. We realize that, if we normalize the market, the equilibrium equity premium is consistent to taking the risk free rate $\rho=0$ in martingale markets. We also observe that the value process affects both the diffusive and rare-event premia except for the CARA negative exponential utility function. The bond price always affect the diffusive risk premium for this risk averse investor.George M. MukupaElias R. OffenEdward M. Lungu
Copyright (c) 2016 Elias Rabson Offen
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2016-11-292016-11-298613910.5539/jmr.v8n6p139Asymptotic Behavior of Higher Order Quasilinear Neutral Difference Equationshttp://www.ccsenet.org/journal/index.php/jmr/article/view/64733
We study, the asymptotic behavior of solutions to a class of higher order quasilinear neutral difference equations under the assumptions that allow applications to even and odd-order difference equations with delayed and advanced arguments, as well as to functional difference equations with more complex arguments that may for instance, alternate infinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.V. SadhasivamPon. SundarA. Santhi
Copyright (c) 2016 V. Sadhasivam, Pon. Sundar, A. Santhi
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2016-11-292016-11-298614810.5539/jmr.v8n6p148Dynamic Behaviors of the Solutions for a Class Delay Harvesting Nicholson's Blowflies Modelhttp://www.ccsenet.org/journal/index.php/jmr/article/view/64734
In this paper, a class of nonlinear delay harvesting Nicholson's blowflies model is considered. Some criteria to ensure the boundedness and oscillation of the solutions for this model are provided. By employing the Lyapunov function, stability of the solutions is also investigated. Moreover, a simulation is given to illustrate our main results.Chunhua FengCarl S. Pettis
Copyright (c) 2016 Chunhua Feng, Carl S. Pettis
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2016-11-292016-11-298616310.5539/jmr.v8n6p163Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 8, No. 6http://www.ccsenet.org/journal/index.php/jmr/article/view/64789
<div><p><em>Journal of Mathematics Research</em> wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.</p><p>Many authors, regardless of whether <em>Journal of Mathematics Research</em> publishes their work, appreciate the helpful feedback provided by the reviewers.</p><p><strong>Reviewers for Volume 8, Number 6</strong></p><p><strong> </strong></p></div><strong><br clear="all" /> </strong><div><p>Abdelaziz Mennouni</p><p>Ali Berkol</p><p>Arman Aghili</p><p>Cecília Rosa</p><p>Chung-Chuan Chen</p><p>David Bartl</p><p>Eric José Avila</p><p>Fei Han</p><p>Gabriela CIUPERCA</p><p>Gane Sam Lo</p><p>Guy Biyogmam</p><p>Jingbo Xia</p><p>K.V.L.N.ACHARYULU</p><p>Khalil Ezzinbi</p><p>Kuldeep Narain Mathur</p><p>Li Wang</p><p>Luca Di Persio</p><p>Marek Brabec</p><p>Muna Abbas</p><p>N. V. Ramana Murty</p><p>Ömür DEVECİ</p><p>Özgür EGE</p><p>Prof. Sanjib Kumar Datta</p><p>R. Roopkumar</p><p>Rovshan Bandaliyev</p><p>Sergiy Koshkin</p><p>Shuhong Chen</p><p>Vishnu Narayan Mishra</p><p>Waleed Al-Rawashdeh</p><p>Xinyun Zhu</p><p>Youssef El-Khatib</p><p>Zoubir DAHMANI</p></div><strong><br clear="all" /> </strong><p><strong> </strong></p><p><strong> </strong></p><p>Sophia Wang</p><p>On behalf of,</p><p>The Editorial Board of <em>Journal of Mathematics Research</em></p><p>Canadian Center of Science and Education</p>Sophia Wang
Copyright (c) 2016 Sophia Wang
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2016-11-302016-11-308617010.5539/jmr.v8n6p169